The Rayleigh distribution is often used where two orthogonal components
have an absolute value, for example, wind velocity and direction may
be combined to yield a wind speed, or real and imaginary components may
have absolute values that are Rayleigh distributed.

The following graph illustrates how the Probability density Function(pdf)
varies with the shape parameter σ:

The Rayleigh distribution is implemented in terms of the standard library
sqrt and exp and as such should have very low
error rates. Some constants such as skewness and kurtosis were calculated
using NTL RR type with 150-bit accuracy, about 50 decimal digits.